A = angle A
B = angle B
C = angle C
a = side a
b = side b
c = side c
P = perimeter
s = semi-perimeter
K = area
r = radius of inscribed circle
R = radius of circumscribed circle
Uses the law of cosines to calculate unknown angles or sides of a triangle. In order to calculate the unknown values you must know and enter 3 known values.
To calculate any angle, A, B or C, enter 3 side lengths a, b and c. This is the same calculation as Side-Side-Side (SSS) Theorem. To calculate a side, say a, enter the opposite angle A and the to other adjacent sides b and c. Using different forms of the law of cosines we can calculate all of the other unknown angles or sides. This is the same calculation as Side-Angle-Side (SAS) Theorem.
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states:\[ a^2 = b^2 + c^2 - 2bc \cos A \] \[ b^2 = a^2 + c^2 - 2ac \cos B \] \[ c^2 = a^2 + b^2 - 2ab \cos C \]
Triangle perimeter, P = a + b + c
Triangle semi-perimeter, s = 0.5 * (a + b + c)
Triangle area, K = √[ s*(s-a)*(s-b)*(s-c)]
Radius of inscribed circle in the triangle, r = √[ (s-a)*(s-b)*(s-c) / s ]
Radius of circumscribed circle around triangle, R = (abc) / (4K)
Zwillinger, Daniel (Editor-in-Chief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 512, 2003.